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I was answering synthetic division example questions and decided to answer it using long division too. The problem is the answers are different.

$$\dfrac{3x^3 – 5x^2 – x + 2} {3x + 1}\tag{1}$$

Synthetic division answer: $3x^2 – 6x + 6$

Long division answer : $x^2 – 2x + 2$

I've thought of dividing $3x^2 – 6x + 6$ by $3$ to give the same answer but I'm not sure if you could do that.

Thanks in advance

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    Hint: To use synthetic division, you divisor must be of the form $x-a$, not $3x-a$ or something like that. To the title, the answer is no. – 2017-02-20
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    Yes, you might've forgotten that Synthetic only works in $x-a$. Meaning if you divided $3x^3-5x^2-x+2$ by $3x+1$, you will get a different answer. – 2017-02-20
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    I answered my synthetic in the form of x–a. I got x= –1/3. But I'm wondering how I could make it the same as my long division answer if they should have the same answers – 2017-02-20

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You just forgot a step. You need to divide by 3 because when you used synthetic division, you solved for $\dfrac{(3x^3-5x^2-x+2)}{(x+1/3)}$ using synthetic division, you have to remember the factor of $3$, so rewrite it as

$\dfrac{(3x^3-5x^2-x+2)}{(x+1/3)} \times \dfrac{1}{3}$ then you can just use it and then divide that answer by $3$.